The Aerodynamic Characteristics of Flaps

The increment A CL' is then
F(6)
A CL' : CL' -- C~ F (A)
F(6) [crC - CLw]
--F(A) g "
CL~ is the lift coefficient of the plain wing at aspect ratio A.
The increment A CL is given by
and hence A CL ---- CL- Cz~,
ACz' --F(A) ~' -- "
(2)
c' F(A) / c' \
It follows that if we can develop a general process for predicting A CL' we should then be able
to determine A CL for the general case of an extending chord flap on a wing of any aspect ratio.*
It may be noted that, unlike A CL', A CL is dependent on incidence for a flap that extends
or reduces the chord, since part of A CL is due to the effective change of chord and is proportional
to wing incidence (i.e., the term containing CL~ in equation (6)). From equation (6)
/
d--~(ACr) = a~ -- 1 , .. . . . . . . . . . . (7)
where a~ is the lift-curve slope of the wing alone. It follows that
C'
a = aw-, . . . . . . . . . . . . . . . . . . (8)
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where a is the lift-curve slope of the wing plus flap.
3.5.1.2. Part-span flaps.--Our usual problem is to derive A CL for a part-span flap given A CL'
for a full-span flap. The simplest procedure is first to derive A CL as if the flaps were full-span and
then to apply a factor for converting the lift increment to that for part-span flaps. This factor,
which is discussed in rather more detail in section 4.1.2, is here denoted by A~(b/b), where b I
is the flap span and b is the wing span. It is represented for various taper ratios by the curves of
Fig. 9. These curves are based on theory 16, 4 checked with experimental results.
We have then
ACz (part-span flaps) = ~3(b/b) ACL (full-span flaps) . . . . . (9)
3.5.2. P#ching moment imrements.--3.5.2.1. Full-span flaps (rectangular wing).--Taking
moments about the extended chord quarter-chord point and reducing the moments to coefficient
form in terms of the extended chord, we easily find that
C,,' = C,, +-~ 1-- c-" " . . . . . . . . .
where C,, and CL are the pitching moment coefficients and lift coefficients referred to the basic
wing chord and quarter-chord point.
But A C,.'= C~ 'l C~[,
where C~ : C~ of the wing with flap retracted.
* Strictly, account should have been taken in the above of the change of effective aspect ratio with the operation
of a flap that extends the chord. The effect is, however, generally small, and in the analysis of a considerable amount of
empirical data it has been found more convenient to ignore it.
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